N-body simulations of exoplanets and their moons

Abstract

The planet-planet interactions in a many-planet system cannot be analytically calculated. Instead, they have to be investigated by using an N-body simulation. I discuss three questions about the N-body interactions in planetary systems: The first two are on the system 55 Cnc, a system with five known planets around a K-type star. I will first simulate the influence, that the other planets have on the transit timing variations of planet e. The second goal is to understand the behaviour of dust in the environment of 55 Cnc e and to estimate if it can be responsible for the variations in the secondary eclipses which have been observed using visible and infrared photometry with CHEOPS and Spitzer. The third goal is to ascertain if the presence of a moon around a planet of the pulsar PSR B1257+12 could be detectable in the pulse arrival timing of its pulses.

I have done simulations on the variation in transit timings of 55 Cnc e to find the influence of the inclination of the orbits of the other planets in the system. The result is that the orbits would have to be at nearly a right angle to have a measurable effect on planet e’s TTVs. Simulations of dust, which planet e might emit, show that the dust can live for several hundred hours. It distributes itself around the star in such a way that it probably does not cause the observed differences in occultation depth. I also simulated the effect a moon around one of the planets of the pulsar PSR B1257+12 would have on the movement of this pulsar. The effect is a measurable signal with an as-yet unidentified hyperperiod. The signal of a moon is different from the signal other sources could produce, such as a fourth planet or the uncertainty of the known planets’ masses. This means that it is feasible that with more sustained observations of PSR B1257+12, exomoons may be detectable in the future.

Popular Abstract

There are planets that do not orbit around the sun but around another star, such planets are called exoplanets. They are difficult to detect since most of them are not bright enough to be directly observed. There are several indirect detection methods such as the ”transit method”, where the planet transits in front of the star and obscures a part of it. This leads to a decrease in the brightness of the star, which can be measured. Another method to detect exoplanets is the ”radial velocity method”. This method uses the fact that the gravity of the planet pulls the star in its direction. The movement of the star causes a change in the observed light due to the Doppler effect. This means that the wavelength of the light changes in dependence on the star’s movement.
Both methods can measure the period of the planet’s orbit and thereby the distance between the star and the planet. The radial velocity method can also measure the mass of the planet if the angle between the orbit and the line of sight is known and the transit method can measure the angle of the orbit. The problem is that not all planets can be observed with both techniques. The planet has to pass directly in front of the star in order to be observed with the transit method and this is only for rather few planets the case.

If several planets are orbiting one star, those planets will interact with each other. Those interactions could result in a small disturbance in the orbit, which could be seen in a slightly changed transit timing. The interactions between the planets depend on the angle at which they stand to each other. This means that it could be possible to determine the angle of the orbits of planets that do not transit by observing one planet in the system that does transit. I will do that in the first part of my thesis by simulating the system called 55 Cnc and determining if the effect of the angle between the planetary orbits is large enough to be observed.

The angle between the planetary orbits is not the only unknown thing in this system. There have been measurements of the ”secondary eclipse” which is in some sense the opposite of a transit: The planet, which reflects light, moves behind the star and the light, that this planet reflects, is no longer visible. This leads to a decrease in the measured brightness. The measurements of the secondary eclipse were different every time it was observed, which is surprising. There is the possibility of dust that surrounds the planet to reflect light from the star. If this dust cloud changes, it would explain, why we see a different amount of light every time. The second part of my thesis is a simulation of the behaviour and lifetime of dust to find out if it could be responsible for the strange measurements.

Since there are many moons orbiting the planets in the solar system, it is reasonable to assume that some if not many exoplanets have moons as well. So far none have been detected because they are much lighter than the planets and therefore harder to detect. I will simulate in the third part of my thesis the effect on the signal, that a moon would have that orbits in the exoplanet system PSR B1257+12.

• author: Schollmeier, Lydia
• supervisor: Jens Hoeijmakers
• organization: Astrophysics; Department of Physics
• course: FYTM06 20231
• year: 2024
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• language: English
• id: 9146340
• date added to LUP: 2024-01-26 09:22:27
• date last changed: 2024-01-26 09:22:27